Problem Solving is the only question type in the GMAT Focus Quantitative Reasoning section: 21 questions in 45 minutes, so about 2 minutes 9 seconds each, with five answer choices and no calculator. Since the Focus Edition dropped geometry, the section leans on arithmetic, algebra, word problems, statistics, counting and number properties. The mathematics rarely goes beyond high school. What makes a question hard is how the information is packaged and how carefully the wrong answers are built.
Almost every wrong choice on a well-written Problem Solving question comes from a specific mistake: answering for the wrong quantity, dropping a condition such as “distinct” or “at least”, adding percentages that should be multiplied, or stopping one step early. Before you calculate, note exactly what is being asked and every constraint. After you calculate, reread the question once before you commit.
Use the answer choices as a tool. When they are far apart, estimate. When the question is full of variables, plug in simple numbers. When a direct count is messy, count the complement and subtract. And when a question is still opaque after 30 seconds, make an educated guess and move on: time spent on one question is taken from the ones you can solve.
The five questions below run from medium to hard. Each explanation names the trap behind the most tempting wrong answer.
5 practice questions
Problem SolvingPercents and Interest ProblemsEasy
Question 1
A jacket is marked at $\$240$. It is sold at a $15\%$ discount, and then an $8\%$ sales tax is charged on the discounted price. What is the final price the customer pays?
A$\$204.00$
B$\$216.00$
C$\$220.32$
D$\$223.20$
E$\$259.20$
Show answer & explanation
Correct answer: C
Key Concept or Approach
Successive percent changes multiply: apply $\times 0.85$ for the discount, then $\times 1.08$ for the tax.
Common trap: 360 - choosing 2 women first and then any 2 of the remaining 9 people, which double-counts committees with 3 or 4 women.
Problem SolvingDivisibility/Multiples/FactorsHard
Question 4
How many positive divisors of $7{,}200$ are multiples of $12$?
A$18$
B$24$
C$27$
D$36$
E$54$
Show answer & explanation
Correct answer: B
Key Concept or Approach
Prime-factorize, then force the divisor to contain $12 = 2^2 \cdot 3$.
Step-by-Step Solution
Step 1: $7200 = 2^5 \cdot 3^2 \cdot 5^2$.
Step 2: A divisor $2^a3^b5^c$ is a multiple of 12 iff $a \ge 2$ and $b \ge 1$: $a \in \{2,3,4,5\}$, $b \in \{1,2\}$, $c \in \{0,1,2\}$.
Step 3: Count: $4 \times 2 \times 3 = 24$.
Final Answer
Answer: B
Common trap: 54 - the total number of divisors of 7,200, ignoring the multiple-of-12 condition.
Problem SolvingMin/Max ProblemsStatistics and Sets ProblemsHard
Question 5
A set of $7$ distinct positive integers has an average (arithmetic mean) of $20$ and a median of $22$. What is the greatest possible value of the largest integer in the set?
A$65$
B$66$
C$68$
D$69$
E$71$
Show answer & explanation
Correct answer: A
Key Concept or Approach
Fix the sum ($7 \times 20 = 140$) and make every other element as small as the constraints allow.
Step-by-Step Solution
Step 1: The three smallest must be distinct positive integers: $1, 2, 3$. The median is $22$.
Step 2: The 5th and 6th elements must exceed $22$ and be distinct: $23, 24$.
